Related papers: Regulating the $P^+ = 0$ Singularity

This paper addresses the controllability of a class of quasi-linear parabolic equations governed by multiplicative controls with mobile support. To prove the existence of such a control forcing the solution to rest at time $T>0$, we first…

We propose a new approach to the spectral theory of perturbed linear operators , in the case of a simple isolated eigenvalue. We obtain two kind of results: ''radius bounds'' which ensure perturbation theory applies for perturbations up to…

We derive in a straightforward way the null controllability of a 1-D heat equation with boundary control. We use the so-called {\em flatness approach}, which consists in parameterizing the solution and the control by the derivatives of a…

This paper aims to answer an open problem posed by Morancey in 2015 concerning the null controllability of the heat equation on (-1, 1) with an internal inverse square potential located at x = 0. For the range of singularity under study,…

In the first part of the paper, we discuss eigenvalue problems of the form -w"+Pw=Ew with complex potential P and zero boundary conditions at infinity on two rays in the complex plane. We give sufficient conditions for continuity of the…

Electronics has changed greatly during recent decades, and some its basic concepts should be revisited. Starting from the sampling procedure, we consider some mathematical, physical and engineering aspects related to singular, mainly…

We propose a new constraint on the structure of strongly coupled field theories. The constraint takes the form of an inequality limiting the number of degrees of freedom in the infrared description of a theory relative to the number of…

We present setups for the practical realization of adding control to unknown subroutines, supplementing the existing quantum optical scheme for black-box control with a counterpart for the quantum control of the ordering of sequences of…

We discuss whether the future extrapolation of the present cosmological state may lead to a singularity even in case of "conventional" (negative) pressure of the dark energy field, namely $w=p/\rho \geq -1$. The discussion is based on an…

This analysis is concerned with the controllability of quantum systems in the case where the standard dipolar approximation, involving the permanent dipole moment of the system, is corrected with a polarizability term, involving the field…

In this paper, we deal with the boundary controllability of a one-dimensional degenerate and singular wave equation with degeneracy and singularity occurring at the boundary of the spatial domain. Exact boundary controllability is proved in…

This is a survey on recent results regarding singularities that occur on higher dimensional stable varieties.

We describe a design methodology for modifying the refractive index profile of graded-index optical instruments that incorporate singularities or zeros in their refractive index. The process maintains the device performance whilst resulting…

Deformation problems with cohomology constraints over a field of characteristic zero are controlled by L-infinity pairs. In this largely expository article we review this theory and focus on recent applications.

Reduction operators, i.e. the operators of nonclassical (or conditional) symmetry of a class of variable coefficient nonlinear wave equations with power nonlinearities is investigated within the framework of singular reduction operator. A…

We extend the recent results concerning boundedness of the maximal regularity operator on tent spaces. This leads us to develop a singular integral operator theory on tent spaces. Such operators have operator-valued kernels. A seemingly…

We study two notions of controllability on a parabolic system with coupling terms of order one. Based on existing results on, on one side parabolic systems with coupling terms of order zero, and on the other one parabolic systems with…

We study the occurrence of number rigidity and deletion singularity in a class of point processes that we call {\it projected perturbed lattices}. These are generalizations of processes of the form…

We investigate near-ring properties that generalize nearfield properties about units. We study zero symmetric near-rings $N$ with identity with two interrelated properties: the units with zero form an additive subgroup of $(N,+)$; the units…

Anisotropic Kepler problem is investigated by perturbation method in both classical and quantum mechanics. In classical mechanics, due to the singularity of the potential, global diffusion in phase space occurs at an arbitrarily small…